What is meant by ‘demineralised’ water and how can it be obtained?

Demineralised water is free from all soluble mineral salts. It does not contain any anions or cations.
Demineralised water is obtained by passing water successively through a cation exchange (in the $H^{+}$ form) and an anion exchange (in the $O{H}^{-}$ form) resin.
During the cation exchange process, $H^{+}$ exchanges for $N{a}^{+},M{g}^{2+},C{a}^{2+}$ and other cations present in water.
$2R{H}_{\left(s\right)}+M_{\left(aq\right)}^{2+}\rightleftharpoons M{R}_{2\left(s\right)}+2H_{\left(aq\right)}^{+}\cdots \left(1\right)$
In the anion exchange process, $O{H}^{-}$ exchanges for anions such as $C{O}_3^{2-},S{O}_4^{2-},C{l}^{-},HC{O}_3^{-}$ etc. present in water.
$RN{H}_{2\left(s\right)}+H_2{O}_{\left(l\right)}\rightleftharpoons RN{H}_3^{+}.O{H}_{\left(s\right)}^{-}$
$RN{H}_3^{+}O{H}_{\left(s\right)}^{-}+X_{\left(aq\right)}^{-}\rightleftharpoons RN{H}_3^{+}.X_{\left(s\right)}^{-}+O{H}_{\left(aq\right)}^{-}\cdots \left(2\right)$
$O{H}^{-}$ ions liberated in reaction (2) neutralize $H^{+}$ ions liberated in reaction (1), thereby forming water.
$H_{\left(aq\right)}^{+}+O{H}_{\left(aq\right)}^{-}\to H_2{O}_{\left(l\right)}$